A bridging model for parallel computation
Communications of the ACM
Implicit representation of graphs
SIAM Journal on Discrete Mathematics
Two linear time Union-Find strategies for image processing
Theoretical Computer Science
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Efficient external memory algorithms by simulating coarse-grained parallel algorithms
Proceedings of the ninth annual ACM symposium on Parallel algorithms and architectures
Minimum Spanning Trees for Minor-Closed Graph Classes in Parallel
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Parallelism in random access machines
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
PRO: A Model for Parallel Resource-Optimal Computation
HPCS '02 Proceedings of the 16th Annual International Symposium on High Performance Computing Systems and Applications
Random Evolution in Massive Graphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Towards realistic implementations of external memory algorithms using a coarse grained paradigm
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartII
Listing all maximal cliques in large sparse real-world graphs
SEA'11 Proceedings of the 10th international conference on Experimental algorithms
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A known approach of detecting dense subgraphs (communities) in large sparse graphs involves first computing the probability vectors for short random walks on the graph, and then using these probability vectors to detect the communities, see Latapy and Pons [2005]. In this paper we focus on the first part of such an approach i.e. the computation of the probability vectors for the random walks, and propose a more efficient algorithm for computing these vectors in time complexity that is linear in the size of the output, in case the input graphs are restricted to a family of graphs of bounded arboricity. Such classes of graphs cover a large number of cases of interest, e.g all minor closed graph classes (planar graphs, graphs of bounded treewidth etc) and random graphs within the preferential attachment model, see Barabási and Albert [1999]. Our approach is extensible to other models of computation (PRAM, BSP or out-of-core computation) and also w.h.p. stays within the same complexity bounds for Erdős Renyi graphs.